A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations

Howard Levine

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 193-198
  • ISSN: 0137-6934

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Levine, Howard. "A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations." Banach Center Publications 33.1 (1996): 193-198. <http://eudml.org/doc/262545>.

@article{Levine1996,
author = {Levine, Howard},
journal = {Banach Center Publications},
keywords = {blow-up rate; global nontrivial solutions},
language = {eng},
number = {1},
pages = {193-198},
title = {A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations},
url = {http://eudml.org/doc/262545},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Levine, Howard
TI - A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 193
EP - 198
LA - eng
KW - blow-up rate; global nontrivial solutions
UR - http://eudml.org/doc/262545
ER -

References

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  1. [A1] D. Aronson, Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967), 890-896. Zbl0153.42002
  2. [A2] D. Aronson, Non-negative solutions of linear parabolic equations, Ann. Scoula Norm. Sup. Pisa 6 (1968), 607-694. Zbl0182.13802
  3. [AW] D. Aronson and H. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math. 30 (1978), 33-76. Zbl0407.92014
  4. [EH] M. Escobedo and M. A. Herrero, Boundedness and blowup for a semilinear reaction-diffusion system, J. Differential Equations 89 (1991), 176-202. Zbl0735.35013
  5. [FLU] M. Fila, H. A. Levine and Y. Uda, A Fujita type global existence-global nonexistence theorem for a system of reaction diffusion equations with differing diffusivities, Math. Methods Appl. Sci. 19 (1994), 809-835. Zbl0814.35046
  6. [Fu] H. Fujita, On the blowing up of solutions of the Cauchy problem for u t = Δ u + u 1 + α , J. Fac. Sci. Univ. Tokyo Sect. IA Math. 16 (1966), 105-113. 
  7. [L1] H. A. Levine, A Fujita type global existence-global nonexistence theorem for a weakly coupled system of reaction-diffusion equations, Z. Angew. Math. Phys. 42 (1992), 408-430. Zbl0786.35075
  8. [L2] H. A. Levine, The role of critical exponents in blow up theorems, SIAM Rev. 32 (1990), 262-288. 
  9. [N] J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954. Zbl0096.06902
  10. [U1] Y. Uda, The critical exponent for a weakly coupled system of generalized Fujita type reaction-diffusion equations, manuscript. Zbl0835.35071
  11. [U2] Y. Uda, Fujita type global existence-global nonexistence theorems for weakly coupled systems of reaction-diffusion equations, PhD dissertation, Iowa State University, 1993. 
  12. [W] F. B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math. 38 (1981), 29-40. Zbl0476.35043

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